This is a minor point, but since Michael Hong brought [into discussion the notation](https://forum.azimuthproject.org/discussion/comment/18388/#Comment_18388), I think the definition:

> for every two objects \\(x,y\\), one specifies an element \\(\mathcal{X}(x,y)\\) of \\(\mathcal{V}\\).

should say "an element \\(\mathcal{X}(x,y)\\) of \\(V\\)" rather than "[...] of \\(\mathcal{V}\\)" (which denotes a tuple, not a set).